Question: Michael is 4 times as old as Jessica. Fifteen years ago, Michael was 9 times as old as Jessica. How old is Jessica now?
Solution: We can use the given information to write down two equations that describe the ages of Michael and Jessica. Let Michael's current age be $m$ and Jessica's current age be $j$ The information in the first sentence can be expressed in the following equation: $m = 4j$ Fifteen years ago, Michael was $m - 15$ years old, and Jessica was $j - 15$ years old. The information in the second sentence can be expressed in the following equation: $m - 15 = 9(j - 15)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $j$ , it might be easiest to use our first equation for $m$ and substitute it into our second equation. Our first equation is: $m = 4j$ . Substituting this into our second equation, we get: $4j$ $-$ $15 = 9(j - 15)$ which combines the information about $j$ from both of our original equations. Simplifying the right side of this equation, we get: $4 j - 15 = 9 j - 135$ Solving for $j$ , we get: $5 j = 120.$ $j = 24$.